Question: Kevin is 8 years older than Michael. For the last four years, Kevin and Michael have been going to the same school. Three years ago, Kevin was 5 times older than Michael. How old is Kevin now?
Answer: We can use the given information to write down two equations that describe the ages of Kevin and Michael. Let Kevin's current age be $k$ and Michael's current age be $m$ The information in the first sentence can be expressed in the following equation: $k = m + 8$ Three years ago, Kevin was $k - 3$ years old, and Michael was $m - 3$ years old. The information in the second sentence can be expressed in the following equation: $k - 3 = 5(m - 3)$ Now we have two independent equations, and we can solve for our two unknowns. Because we are looking for $k$ , it might be easiest to solve our first equation for $m$ and substitute it into our second equation. Solving our first equation for $m$ , we get: $m = k - 8$ . Substituting this into our second equation, we get the equation: $k - 3 = 5($ $(k - 8)$ $ -$ $ 3)$ which combines the information about $k$ from both of our original equations. Simplifying the right side of this equation, we get: $k - 3 = 5k - 55$ Solving for $k$ , we get: $4 k = 52$ $k = 13$.